the prometheans were a specific group of forerunners dedicated to war, eventually when the didact composed all of his follower prometheans(forerunner) and then when he tried to compose the humans, the name got carried over to include both parties

No, the experiment that failed was when the forerunners attempted to escape the flood by using the composer to escape as data, remove the flood, and then return to organic forms, essentially being immortal in the process. this was tested, but the personalities stored as data fragmented, and when returned, created the abominations of the kind later used as knights. the didact realized that while the composer could not be used to make the forerunners immortal, or save them from the flood directly, he realized that the composer could be used to create knights invulnerable to flood contamination. then he composed the promethean forerunners, and then the humans, and THEN (a few million years later) the station around Halo 03, and THEN the city of New Phoenix.

anyway, the composed that went wrong were those they hoped to bring back in their natural forms, not the forerunners or humans, which they intended to create knights with.

The Prometheans were the highest and most respected group of Warrior-Servants in the Forerunner Ecumene.[1] The Didact and Confirmer were Prometheans. Physically, Prometheans were the highest form a Warrior-Servant could mutate to, standing around four meters tall and between 800 and 1,000 kilograms in weight. They were heavily muscled, their hands capable of easily crushing a human skull.

The main enemies in Halo 4, introduced as a new class of opponents are the Promethean Knights, Crawlers, Watchers and a Forerunner Promethean known as The Didact.

The Librarian reveals to the Master Chief that some of the Prometheans are humans, transformed by the Didact by means of a device known as "The Composer". When the Encumene discovered Didact's plan to turn all of humanity into Prometheans to gain immunity to the Flood, halo.wikia.com/wiki/Promethean

Note where it says some Prometheans are human, and where it also calls the Diadect a Promethean forerunner

its getting the info from a book Halo: Cryptum (which is a good book). It also says that the prometheans are the super warriors, the most exalted of all warriors in the caste. You ought to read it, I really enjoyed it. and just google it, there are plenty of sources to support what i am saying